A man of weight W is standing on a lift which is moving upward with an acceleration a. The apparent wieght of the man is

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thats how the FBD for the man will be.
now, Fn is responsible for man's acceleration a upwards. which means that Fn will have to be greater than W, his real weight. (or else u'll find the man sinking down, while the lift accelerates upwards)
so this gives us Fn > W
u know that the weight we measure using a weighing machine is actually the measure of the normal force it exerts on us, right? so the apparent weight = Fn
hence, apparent weight > real weight W
u got it?

In this case, the elevator and the person are starting from rest at a lower floor. The elevator accelerates upward. The inertia of the person would prefer to stay stationary, so the elevator floor and scale must push up on the person to accelerate him upward along with the elevator.
Let's consider Newton's 2nd Law (ΣF=ma) acting on the person. The overall acceleration of the person is upward (with the elevator). So ma is positive (upward). The only external forces acting on the person are the force of gravity acting down (-W=-mg) and the supporting Normal Force FN that the scale applies upward on the person. So ΣF=ma= -mg+FN . We want to know FN because that is the number that we read off the scale. FN =mg+ma, which is GREATER than the true weight.